Structured light three-dimensional reconstruction system calibration method of polynomial constraint angular points

Abstract

The invention relates to the technical field of structured light three-dimensional reconstruction systems, in particular to a structured light three-dimensional reconstruction system calibration method of polynomial constraint angular points, which comprises the following steps: extracting actual camera angular points and actual projector angular points based on a calibration board; calibrating the camera to obtain an actual camera projection matrix; constructing a polynomial representing a distribution relationship among the angular point groups of the projector, calibrating the projector under the constraint of the polynomial, and obtaining a constrained projector projection matrix; and calculating a three-dimensional reconstruction error based on the actual camera angular point, the actual projector angular point, the actual camera projection matrix and the constrained projector projection matrix, and determining a final polynomial and an optimal projector angular point calibration parameter according to the error. The calibration effect is improved by enhancing the relation between the angle point groups of the projector, and then the measurement precision of the structured light system is improved.

Description

Technical Field

[0001] The present invention relates to the technical field of structured light three-dimensional reconstruction systems, and in particular to a calibration method for structured light three-dimensional reconstruction systems with polynomial constrained corner points. Background Art

[0002] Structured light is a mainstream technology for optical 3D reconstruction, offering a good balance between flexibility and measurement accuracy. Its core approach is to utilize the phase mapping relationship between camera image pixels and projector image pixels, along with information about the camera's and projector's intrinsic and extrinsic parameters, to determine the 3D information of any point on an object's surface. Therefore, the calibration accuracy of a structured light 3D reconstruction system is crucial to the system's measurement accuracy. Camera calibration methods are relatively mature, with Zhang's calibration method being the most commonly used. The steps generally include corner detection, calculation of extrinsic and extrinsic parameters, and determination of distortion coefficients. Projector calibration methods are similar, but unlike cameras that can directly capture images, projectors cannot directly acquire corners.

[0003] The more classic method for projector calibration is the implicit calibration technology, which establishes a model by mapping the relationship between the height modulation phase relative to the reference plane and the depth of the object. However, this method is subject to geometric limitations and strictly requires that the optical axes of the camera and projector are perpendicular to the reference plane or the line connecting the optical centers is parallel to the reference plane. Another method is to treat the projector as an inverse camera based on the principle of optical path reversibility, and map the camera pixels to the projector pixels based on the absolute phase obtained by solving the projected fringe pattern. Finally, calibration and three-dimensional reconstruction are performed. Although this method is not applicable to structured lighting equipment that cannot be modeled by inverse camera, since the calibration of the camera and projector are performed independently, the calibration of the projector does not need to consider the internal and external parameters of the camera, avoiding error propagation. In addition, some scholars have abandoned the inherent internal and external parameters and directly established a mathematical model of pixel coordinates combined with phase to directly obtain the three-dimensional information of the object. However, this type of method has many coefficients to be calibrated and the workload is large. Therefore, the present invention proposes a calibration method for a structured light three-dimensional reconstruction system with polynomial constrained corners. Summary of the Invention

[0004] The purpose of this invention is to address the problem that most current methods focus on establishing a complex model of the structured light system without considering the impact of the relationship between corner point groups on the calibration results. This invention provides a calibration method for a structured light 3D reconstruction system with polynomial constrained corner points, which improves the calibration effect by strengthening the relationship between projector corner point groups, thereby improving the measurement accuracy of the structured light system.

[0005] To achieve the above object, the present invention provides the following solutions:

[0006] A polynomial constrained corner point structured light 3D reconstruction system calibration method includes:

[0007] Extract actual camera corner points and actual projector corner points based on the calibration plate;

[0008] Calibrate the camera and obtain the actual camera projection matrix;

[0009] Constructing a polynomial representing the distribution relationship between projector corner point groups, calibrating the projector under the constraints of the polynomial to obtain a constrained projector projection matrix;

[0010] A three-dimensional reconstruction error is calculated based on the actual camera corner points, the actual projector corner points, the actual camera projection matrix, and the constrained projector projection matrix, and a final polynomial and optimal projector corner point calibration parameters are determined according to the error.

[0011] Optionally, extracting actual camera corner points and actual projector corner points based on the calibration plate includes:

[0012] Scanning the calibration plate to obtain an image of the calibration plate;

[0013] The actual camera corner points are extracted from the calibration plate image, and the absolute phase obtained by fringe decoding is used to obtain the actual projector corner points according to the actual camera corner points.

[0014] Optionally, the relationship between the actual camera corner point and the actual projector corner point is:

[0015]

[0016] Among them, (u c ,v c ) is the pixel coordinate of the object on the camera side, is the absolute phase of the object corresponding to the pixel coordinate at the camera end, (u p ,v p ) is the pixel coordinate of the object on the projector side, is the absolute phase of the object corresponding to the pixel coordinate at the projector end, and W is the field width of the coding stripes.

[0017] Optionally, calibrating the camera to obtain the actual camera projection matrix includes:

[0018] The camera is calibrated using the Zhang Zhengyou calibration method to obtain internal and external parameters;

[0019] The product of the internal and external parameters is calculated to obtain the actual camera projection matrix.

[0020] Optionally, constructing a polynomial representing the distribution relationship between projector corner point groups, calibrating the projector under the constraints of the polynomial, and obtaining the constrained projector projection matrix includes:

[0021] Determine the polynomial structure and coefficients according to the actual camera projection matrix, and construct a plurality of polynomials;

[0022] Constrained projector corner points are obtained according to the polynomial, and the projector is calibrated using the constrained projector corner points to obtain a plurality of constrained projector projection matrices.

[0023] Optionally, a method for obtaining the constrained projector corner point according to the polynomial is:

[0024]

[0025] in, are the constrained projector corner coordinates, f and g are the coordinates Two fitting polynomials, p and q are the coefficients of polynomial f and polynomial g, i and j, m and n are the ideal world coordinates X in polynomial f and polynomial g respectively. W and Y W The terms of I and J are the ideal world coordinates X in the polynomial f. W and Y W The maximum term, M and N are the ideal world coordinates X in the polynomial g. W and Y W The maximum term, p ij and q mn are the coefficients of polynomial f and polynomial g at different orders, and are the world coordinates under item i and j respectively, and are the world coordinates under items m and n respectively.

[0026] Optionally, calculating the three-dimensional reconstruction error based on the actual camera corner point, the actual projector corner point, the actual camera projection matrix, and the constrained projector projection matrix to obtain a final polynomial and optimal projector corner point calibration parameters includes:

[0027] Performing three-dimensional reconstruction based on the actual camera corner points, the actual projector corner points, the actual camera projection matrix, and the constrained projector projection matrix to obtain a number of new world coordinates;

[0028] Calculate the error between each new world coordinate and the ideal world coordinate, and select the final polynomial and the optimal projector corner calibration parameters.

[0029] Optionally, the method for calculating the error between the new world coordinates and the ideal world coordinates is:

[0030]

[0031] Among them, (X W ,YW ,Z W ) is the ideal world coordinate, is the new world coordinate, TDRE is the error, t is the current corner point, and T is the number of corner points.

[0032] The beneficial effects of the present invention are:

[0033] Based on the judgment that there is a certain connection between the distribution of image pixel coordinates obtained by reprojecting uniformly distributed world coordinates, the present invention provides a calibration method for a structured light 3D reconstruction system with polynomially constrained corner points. By strengthening the relationship between projector corner point groups, the calibration effect is improved, thereby improving the measurement accuracy of the structured light system. The distribution of the corrected projector corner points can be made to conform to a certain pattern, and the mapping with the world coordinates is more reasonable. BRIEF DESCRIPTION OF THE DRAWINGS

[0034] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0035] Figure 1 This is a flow chart of a method for calibrating a structured light 3D reconstruction system using polynomially constrained corner points according to an embodiment of the present invention;

[0036] Figure 2 Schematic diagram of the structure of a three-dimensional structured light measurement system according to an embodiment of the present invention;

[0037] Figure 3 The calibration plate pattern captured by the camera of an embodiment of the present invention and the extracted corner points;

[0038] Figure 4 This is a TDRE scatter plot obtained by calibrating different corner points of the camera and left projector according to an embodiment of the present invention;

[0039] Figure 5 This is a TDRE scatter plot obtained by calibrating different corner points of the camera and left projector according to an embodiment of the present invention;

[0040] Figure 6 Schematic diagram of a standard sphere with a radius of 19.0535 in an embodiment of the present invention;

[0041] Figure 7 Schematic diagram of the sphere radius measurement results of the structured light system calibrated at different corner points according to an embodiment of the present invention. DETAILED DESCRIPTION

[0042] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0043] In order to make the above-mentioned objects, features and advantages of the present invention more obvious and easy to understand, the present invention is further described in detail below with reference to the accompanying drawings and specific embodiments.

[0044] This embodiment provides a method for calibrating a structured light 3D reconstruction system with polynomial constrained corner points, including:

[0045] Extract actual camera corner points and actual projector corner points based on the calibration plate;

[0046] Calibrate the camera and obtain the actual camera projection matrix;

[0047] Constructing a polynomial representing the distribution relationship between projector corner point groups, calibrating the projector under the constraints of the polynomial to obtain a constrained projector projection matrix;

[0048] A three-dimensional reconstruction error is calculated based on the actual camera corner points, the actual projector corner points, the actual camera projection matrix, and the constrained projector projection matrix, and a final polynomial and optimal projector corner point calibration parameters are determined according to the error.

[0049] Specifically, when calibrating a projector using the inverse camera method, the projector corner points obtained by mapping the camera corner points will also carry certain errors due to phase errors. This makes the distribution of the projector corner points relatively irregular, directly affecting the measurement accuracy of the structured light system. To address this issue, this embodiment provides a method for calibrating a structured light 3D reconstruction system using polynomially constrained corner points, based on the assumption that the distribution of image pixel coordinates obtained by reprojecting uniformly distributed world coordinates is somewhat related. This method improves the calibration effect by strengthening the relationship between projector corner point groups, thereby improving the measurement accuracy of the structured light system. This ensures that the distribution of the corrected projector corner points conforms to a certain pattern, and the mapping to the world coordinates is more reasonable.

[0050] The following combination Figure 1 The calibration method of the structured light 3D reconstruction system for polynomial constrained corner points provided in this embodiment is described in detail, and specifically includes the following steps:

[0051] Step 1: Extract the actual camera corner points and actual projector corner points based on the calibration plate.

[0052] Step 2: Calibrate the camera to obtain the actual camera projection matrix.

[0053] Step 3: Construct a polynomial representing the distribution relationship between the projector corner point groups, calibrate the projector under the constraints of the polynomial, and obtain the constrained projector projection matrix;

[0054] Step 4: Calculate the 3D reconstruction error based on the actual camera corner points, the actual projector corner points, the actual camera projection matrix, and the constrained projector projection matrix, and determine the final polynomial and the optimal projector corner point calibration parameters based on the error.

[0055] Specifically, without considering the distortion, the pixel coordinates (u, v) and the world coordinates (X W ,Y W ,Z W ) has the following conversion relationship:

[0056]

[0057] Where s is the scale factor, f x With f y are the ratios of the camera focal length f to the pixel physical size dx and dy, respectively. (u0, v0) is the origin of the coordinate system in the image coordinate system. R 3×3 is the rotation matrix, T 3×1 is the translation matrix, and the projection matrix A is the product of the intrinsic and extrinsic parameter matrices. In this embodiment, these parameters are all obtained by the Zhang calibration method, and the only difference is the pixel coordinates of the corner points used.

[0058] According to formula (1), this conversion relationship includes two key steps:

[0059] 1) External parameter transformation: transform the point (X W ,Y W ,Z W ) is converted to a point in the camera coordinate system (X C ,Y C ,Z C ).

[0060] 2) Intrinsic parameter transformation: Project the 3D point in the camera coordinate system to the image plane pixel point (u, v).

[0061] The intrinsic matrix is usually linear, meaning it only scales and translates the camera coordinates. The rotation and translation matrices of the extrinsic matrix also act linearly. However, the key lies in perspective projection. Perspective projection has nonlinear properties when converting 3D coordinates to 2D coordinates. This is because perspective transformation involves projecting a 3D point by dividing its depth:

[0062]

[0063] Therefore, after perspective transformation, even if the given world coordinates are linearly distributed in space, the image pixel coordinates (u, v) will show a nonlinear relationship. However, the relationship between the pixel coordinates of the camera and projector and the world coordinates is as follows:

[0064]

[0065] exist Figure 2 In the structured light system shown, the camera corner points extracted based on grayscale changes generally maintain a certain connection, but the projector corner points are mapped based on the camera corner points. This mapping process involves phase, which is easily affected by many factors. This results in the mapped projector corner points not being the correct corner points, and the relationship between them is not necessarily correct. Using these corner points to calibrate the projector may affect the system accuracy.

[0066] Therefore, this embodiment intends to find a polynomial to strengthen the distribution relationship between projector corner point groups. Considering that pixel corner points can be converted from world coordinate corner points, the following relationship is established:

[0067]

[0068] In the formula is the constrained projector corner coordinate, p and q are the coefficients of the polynomial, i and j, m and n are the ideal world coordinates X in their respective polynomials. W and Y W Considering that the inherent properties of each camera and projector are different, the traversal method is used to determine the polynomial in the actual calibration process. In order to reduce the number of cycles, I = M, J = N. The specific calibration process is as follows Figure 1 shown.

[0069] The 3D reconstruction formula used in the calibration process:

[0070]

[0071] Three-dimensional reconstruction error TDRE:

[0072]

[0073] Furthermore, in step 1 and step 2, extracting the actual camera corner points and the actual projector corner points based on the calibration plate includes: scanning the calibration plate to obtain the calibration plate image; extracting the actual camera corner points from the calibration plate image, and using the absolute phase obtained by fringe decoding to obtain the actual projector corner points according to the actual camera corner points.

[0074] Calibrating the camera to obtain the actual camera projection matrix includes: calibrating the camera using the Zhang Zhengyou calibration method to obtain internal and external parameters; and calculating the product of the internal and external parameters to obtain the actual camera projection matrix.

[0075] Specifically, in this embodiment, the calibration plate is placed on the scanning table and rotated to take 15 pictures, of which four pictures are as follows: Figure 3 As shown in Figure 1, the circles are the extracted corner points. Camera calibration is performed, and the selected internal and external parameters are shown in Table 1.

[0076] Table 1

[0077]

[0078] According to the calibration parameters and formula (1), A is obtained c ,In addition, the projector corner points need to be obtained based on the camera corner points.

[0079] Among the current methods for obtaining projector corner points, the most common method is to use the absolute phase obtained by fringe decoding for mapping: the object corresponds to the pixel (u c ,v c )'s absolute phase The corresponding pixel on the projector side (u p ,v p )'s absolute phase is consistent:

[0080]

[0081] Since the fringe image of the projector is composed of uniform stripes, we can get:

[0082]

[0083] Formula (8) establishes the pixel coordinates (u c ,v c ) and the projector pixel coordinates (u p ,v p ), where W is the field of view width of the coding stripes. The key to this relationship is the acquired phase. Currently, the structured light 3D reconstruction system often uses the N-step phase shift method:

[0084]

[0085] Where I n is the image after n-step phase shift, I a is the background light intensity, I b is the modulated light intensity, (u,v) is the pixel coordinate, is the phase corresponding to the pixel coordinate, which can be reconstructed as follows:

[0086]

[0087] The phase obtained by formula (10) is wrapped in (-π,π], and the absolute phase can be obtained by using multi-frequency heterodyne or Gray code to determine whether the decoded fringe belongs to the kth period:

[0088]

[0089] Therefore, when the camera captures the fringe image projected by the projector and decodes it, the corresponding projector pixel can be obtained using formula (8) based on the camera pixel and the phase value of the point.

[0090] Furthermore, in step 3, a polynomial representing the distribution relationship between projector corner point groups is constructed, and the projector is calibrated under the constraints of the polynomial to obtain a constrained projector projection matrix, including: determining the polynomial structure and coefficients according to the actual camera projection matrix, and constructing several polynomials; obtaining the constrained projector corner points according to the polynomial, and calibrating the projector using the constrained projector corner points to obtain several constrained projector projection matrices.

[0091] Specifically, in step 3 of this embodiment, a polynomial is obtained. First, the structure of the polynomial is determined by different I and J. In order to avoid a large change in the position of the corner point, the least squares method is used to obtain the coefficients of the polynomial:

[0092]

[0093] Furthermore, in step 4, the three-dimensional reconstruction error is calculated based on the actual camera corner points, the actual projector corner points, the actual camera projection matrix, and the constrained projector projection matrix, and the final polynomial and the optimal projector corner point calibration parameters are obtained, including: performing three-dimensional reconstruction based on the actual camera corner points, the actual projector corner points, the actual camera projection matrix, and the constrained projector projection matrix to obtain several new world coordinates; calculating the error between each new world coordinate and the ideal world coordinate, and selecting the final polynomial and the optimal projector corner point calibration parameters.

[0094] Specifically, in step 4, this embodiment uses each polynomial to obtain the constrained projector corner coordinates Calibrate the projector separately to obtain the projection matrix Use the actual camera corners (u c ,v c ), actual projector corner point (u p ,v p ), the actual camera projection matrix A c , the projection matrix obtained by constrained projector corner calibration To obtain the new world coordinates according to formula (5) And calculate the TDRE with the ideal world coordinates.

[0095] Since each image can obtain its own extrinsic parameters, the mean 3D reconstruction error (MTDRE) is used as the evaluation metric. The statistical results of MTDRE for corner point constraints on the left projector under different I and J are shown in Table 2, and the statistical results of MTDRE for corner point constraints on the right projector are shown in Table 3.

[0096] Table 2

[0097] J＝1 J＝2 J＝3 J＝4 J＝5 I＝1 167.308 2.2811 2.24311 2.2495 2.2477 I＝2 1.2933 0.1025 0.1402 0.1381 0.1396 I＝3 1.2496 0.1063 0.1423 0.1432 0.1423 I＝4 1.2493 0.1057 0.1434 0.1431 0.1422 I＝5 1.2519 0.1064 0.1432 0.1423 0.1418

[0098] Table 3

[0099] J＝1 J＝2 J＝3 J＝4 J＝5 I＝1 204.889 2.0938 1.9923 1.9934 1.9856 I＝2 1.4079 0.0783 0.1680 0.1671 0.1657 I＝3 1.3455 0.1095 0.1744 0.1735 0.1706 I＝4 1.3393 0.1082 0.1742 0.1742 0.1719 I＝5 1.3411 0.1075 0.1719 0.1706 0.1707

[0100] According to Table 2 and Table 3, when I = J = 2, the calibration results of the left and right projectors after corner point constraint are the lowest, the former is 0.1025mm, and the latter is 0.0783mm. In this case, the polynomial is:

[0101]

[0102] At this time, the optimal constrained left projector corner calibration parameters and the optimal right projector corner calibration parameters are shown in Table 4 and Table 5 respectively.

[0103] Table 4

[0104]

[0105] Table 5

[0106]

[0107] In order to verify the effectiveness of this method, the actual projector corner points are used for direct calibration, and the TDRE calculated based on the external parameters obtained for each image is statistically analyzed. At the same time, similar constraint experiments are also performed on the camera corner points. The 3D reconstruction error TDRE obtained by calibrating different corner points of the camera and the left projector is as follows: Figure 4 As shown, the 3D reconstruction error TDRE obtained by calibrating different corner points of the camera and the right projector is as follows: Figure 5 shown.

[0108] Figure 4 and Figure 5 Cam and CamR represent the actual camera corner calibration and the constrained camera corner calibration, LProj and LprojR represent the actual left projector corner calibration and the constrained left projector corner calibration, RProj and RprojR represent the actual right projector corner calibration and the constrained right projector corner calibration. Figure 4 and Figure 5Regardless of whether the left or right projector is calibrated using constrained projector corners, the TDRE is effectively reduced compared to calibration using the actual projector corners. The MTDRE for different corner calibrations is shown in Table 3. According to Table 6, "Cam&LprojR" and "Cam&RprojR," which constrain projector corners, both achieve the best performance, achieving reductions of 0.03897mm and 0.09198mm, respectively, compared to "Cam&Lproj" and "Cam&RprojR," which both use actual corners. However, constraining camera corners does not yield much improvement. The actual left projector corner calibration parameters used are shown in Table 7, and the actual right projector corner calibration parameters used are shown in Table 8.

[0109] Table 6

[0110] LProj LProjR RProj RProjR Cam 0.14144 0.10247 0.17026 0.07828 CamR 0.14141 0.10326 0.16860 0.07893

[0111] Table 7

[0112]

[0113] Table 8

[0114]

[0115] In order to further verify the effectiveness of this method, Figure 6 The radius of the standard ball shown is measured to measure the system accuracy of different corner point calibrations. The actual radius of the standard ball is 19.0535mm. The specific measurement results are shown in Figure 7 .

[0116] according to Figure 7 In the camera-left projector system, the sphere radius measurement result is 0.0909mm when using the actual corner calibration parameters, which is already quite accurate. However, after using the constrained left projector corner calibration parameters, the sphere radius measurement result is reduced by 0.0618mm, and the accuracy is improved by 67.99%. If the camera corners are constrained, there is a slight improvement, but the effect is not significant. In practice, considering the time cost, it is not necessary to consider constraining the camera corners. In the camera-right projector system, the sphere radius measurement result is 0.4133mm when using the actual corner calibration parameters, which has a large error. However, after using the constrained right projector corner calibration parameters, the measurement result is directly reduced to 0.0665mm, and the accuracy is improved by 83.90%. This experiment directly verifies the effectiveness of this method.

[0117] The embodiments described above are merely descriptions of preferred embodiments of the present invention and are not intended to limit the scope of the present invention. Without departing from the spirit of the present invention, various modifications and improvements made to the technical solutions of the present invention by persons skilled in the art should fall within the scope of protection defined by the claims of the present invention.

Claims

1. A polynomial constrained corner point structured light 3D reconstruction system calibration method, characterized by: include: Extract actual camera corner points and actual projector corner points based on the calibration plate; Calibrate the camera and obtain the actual camera projection matrix; Constructing a polynomial representing the distribution relationship between projector corner point groups, calibrating the projector under the constraints of the polynomial to obtain a constrained projector projection matrix; A three-dimensional reconstruction error is calculated based on the actual camera corner points, the actual projector corner points, the actual camera projection matrix, and the constrained projector projection matrix, and a final polynomial and optimal projector corner point calibration parameters are determined according to the error.

2. The polynomial constrained corner point structured light 3D reconstruction system calibration method according to claim 1, characterized in that: Extracting actual camera corner points and actual projector corner points based on the calibration plate includes: Scanning the calibration plate to obtain an image of the calibration plate; The actual camera corner points are extracted from the calibration plate image, and the absolute phase obtained by fringe decoding is used to obtain the actual projector corner points according to the actual camera corner points.

3. The polynomial constrained corner point structured light 3D reconstruction system calibration method according to claim 2, characterized in that: The relationship between the actual camera corner point and the actual projector corner point is: Among them, (u c ,v c ) is the pixel coordinate of the object at the camera end, φ c is the absolute phase of the object corresponding to the pixel coordinate at the camera end, (u p ,v p ) is the pixel coordinate of the object at the projector end, φ p is the absolute phase of the object corresponding to the pixel coordinate at the projector end, and W is the field width of the coding stripes.

4. The polynomial constrained corner point structured light 3D reconstruction system calibration method according to claim 1, characterized in that: Calibrate the camera to obtain the actual camera projection matrix including: The camera is calibrated using the Zhang Zhengyou calibration method to obtain internal and external parameters; The product of the internal and external parameters is calculated to obtain the actual camera projection matrix.

5. The polynomial constrained corner point structured light 3D reconstruction system calibration method according to claim 1, characterized in that: Constructing a polynomial representing the distribution relationship between projector corner point groups, calibrating the projector under the constraints of the polynomial, and obtaining the constrained projector projection matrix includes: Determine the polynomial structure and coefficients according to the actual camera projection matrix, and construct a plurality of polynomials; Constrained projector corner points are obtained according to the polynomial, and the projector is calibrated using the constrained projector corner points to obtain a plurality of constrained projector projection matrices.

6. The polynomial constrained corner point structured light 3D reconstruction system calibration method according to claim 5, characterized in that: The method for obtaining the constrained projector corner points according to the polynomial is: in, are the constrained projector corner coordinates, f and g are the coordinates Two fitting polynomials, p and q are the coefficients of polynomial f and polynomial g, i and j, m and n are the ideal world coordinates X in polynomial f and polynomial g respectively. W and Y W The terms of I and J are the ideal world coordinates X in the polynomial f. W and Y W The maximum term, M and N are the ideal world coordinates X in the polynomial g. W and Y W The maximum term, p ij and q mn are the coefficients of polynomial f and polynomial g at different orders, and are the world coordinates under item i and j respectively, and are the world coordinates under items m and n respectively.

7. The polynomial constrained corner point structured light 3D reconstruction system calibration method according to claim 1, characterized in that: Calculating a three-dimensional reconstruction error based on the actual camera corner point, the actual projector corner point, the actual camera projection matrix, and the constrained projector projection matrix to obtain a final polynomial and optimal projector corner point calibration parameters includes: Performing three-dimensional reconstruction based on the actual camera corner points, the actual projector corner points, the actual camera projection matrix, and the constrained projector projection matrix to obtain a number of new world coordinates; Calculate the error between each new world coordinate and the ideal world coordinate, and select the final polynomial and the optimal projector corner calibration parameters.

8. The polynomial constrained corner point structured light 3D reconstruction system calibration method according to claim 7, characterized in that: The method for calculating the error between the new world coordinates and the ideal world coordinates is: Among them, (X W ,Y W ,Z W ) is the ideal world coordinate, is the new world coordinate, TDRE is the error, t is the current corner point, and T is the number of corner points.

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